EasyFit – Easily Fit Distributions to Your Data!

# Chi-Squared Distribution

## Parameters

- degrees of freedom (positive integer)
- continuous location parameter ( yields the one-parameter Chi-Squared distribution)

## One-Parameter Chi-Squared Distribution

### Cumulative Distribution Function

where is the Gamma Function,  and is the Incomplete Gamma Function.

## Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

 Description VBA Functions Worksheet Functions Distribution Fitting - ``` =DistFit("ChiSqr";Data;[Options]```1```) ``` Probability Density Function `ChiSqrPdf(x,nu,[gamma])` ``` =ChiSqrPdf(nu;[gamma]) =DistPdf("ChiSqr(nu;[gamma])";x) ``` Cumulative Distribution Function `ChiSqrCdf(x,nu,[gamma])` ``` =ChiSqrCdf(nu;[gamma]) =DistCdf("ChiSqr(nu;[gamma])";x) ``` Survival Function `ChiSqrSurv(x,nu,[gamma])` ``` =DistSurv("ChiSqr(nu;[gamma])";x) ``` Hazard Function `ChiSqrHaz(x,nu,[gamma])` ``` =ChiSqrHaz(nu;[gamma]) =DistHaz("ChiSqr(nu;[gamma])";x) ``` Cumulative Hazard Function `ChiSqrCumHaz(x,nu,[gamma])` ``` =DistCumHaz("ChiSqr(nu;[gamma])";x) ``` Inverse CDF (Quantile Function) `ChiSqrInv(P,nu,[gamma])` ``` =ChiSqrInv(nu;[gamma]) =DistInv("ChiSqr(nu;[gamma])";P) ``` Random Numbers `ChiSqrRand(nu,[gamma])` ``` =ChiSqrRand(nu;[gamma]) =DistRand("ChiSqr(nu;[gamma])") ``` Mode `ChiSqrMode(nu,[gamma])` ``` =DistMode("ChiSqr(nu;[gamma])") ``` Mean `ChiSqrMean(nu,[gamma])` ``` =ChiSqrMean(nu;[gamma]) =DistMean("ChiSqr(nu;[gamma])") ``` Variance `ChiSqrVar(nu,[gamma])` ``` =ChiSqrVar(nu;[gamma]) =DistVar("ChiSqr(nu;[gamma])") ``` Standard Deviation `ChiSqrStdev(nu,[gamma])` ``` =ChiSqrStdev(nu;[gamma]) =DistStdev("ChiSqr(nu;[gamma])") ``` Skewness `ChiSqrSkew(nu,[gamma])` ``` =DistSkew("ChiSqr(nu;[gamma])") ``` (Excess) Kurtosis `ChiSqrKurt(nu,[gamma])` ``` =DistKurt("ChiSqr(nu;[gamma])") ```

1. The `Options` parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
2. The `gamma` parameter is optional (the default value is 0).